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Find the derivative $\frac{d}{dx}\left(\frac{y-x}{y+x}\right)$

Used Formulas

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Solving: $\frac{d}{dx}\left(\frac{y-x}{y+x}\right)$
Solve instead: $\frac{dy}{dx}\cdot\frac{y-x}{y+x}$

Solution

Formulas

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Basic Derivatives

· Quotient Rule in Differentiation
$\frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$
· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$
· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$

Function Plot

Plotting: $\frac{-y-x-y+x}{\left(y+x\right)^2}$

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0
a
b
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n
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y
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◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Quotient Rule of Differentiation

The quotient rule is a formal rule for differentiating problems where one function is divided by another.

Used Formulas

See formulas (5)

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